Question

Each equation given below describes a parabola. Which statement best compares their graphs?

y = -3x2 y= -7x2

A. Both parabolas open downward, and y = -7x2 is wider than y = -3x2.
B. Both parabolas open downward, and y = -3x2 is wider than y = -7x2.
C. Both parabolas open to the left, and y = -3x2 is wider than y = -7x2.
D. Both parabolas open to the left, and y = -7x2 is wider than y = -3x2.

Answer 1

The answer would be B. Both parabolas open downward, and y = -3x2 is wider than y = -7x2.

Answer 2

Answer:  The correct statement is (B). Both parabolas open downward, and $y=-3x^2$ is wider than $y=-7x^2.$

Step-by-step explanation:  The equations of the two parabolas are as follows:

$y=-3x^2~~~~~~~~~~~~~(i)\\y=-7x^2~~~~~~~~~~~~~(ii)$

The standard equation of a parabola is given by

$y=a(x-h)^2+k.$

If a < 0, then the parabola open downwards and if a > 0, then the parabola open upwards.

From equation (i), we have

$y=-3x^2\\\\\Rightarrow y=-3(x-0)^2+0,$

so a = -3 < 0, so the parabola (i) open downwards.

From equation (ii), we have

$y=-7x^2\\\\\Rightarrow y=-7(x-0)^2+0,$

so a = -7 < 0, so the parabola (ii) open upwards.

Also, since -3 > -7, so the parabola (i) is wider than the parabola (ii).

Therefore, both parabolas open downward, and $y=-3x^2$ is wider than $y=-7x^2.$

The graphs of the parabolas are shown in the attached figure.

Thus, (B) is the correct ption.